Lattice Models and Agent-Based Models in Biology: Linking Individual Properties to Population Properties

Wednesday, June 16 at 04:15am (PDT)
Wednesday, June 16 at 12:15pm (BST)
Wednesday, June 16 08:15pm (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS12" time block.
Note: this minisymposia has multiple sessions. The second session is MS13-CBBS (click here).

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Bhargav Karamched (Florida State University, United States of America)


Lattice models have a rich history in biological modeling. They provide a valuable framework for modeling complex spatiotemporal dynamics in biological tissues. Agent-based models provide realistic models of biological tissues and populations. Both have been used to model protein folding, cancer initiation and progression, and motor protein transport through a cell, amongst numerous other applications. Both frameworks have the important property of linking individual properties to population-level structure. Spatiotemporal dynamics in biological systems are often modeled by partial differential equations. Partial differential equation models offer scope for analysis, but they often coarse grain dynamics so that an individual's impact on the population is unclear. Lattice models are a viable alternative to the aforementioned. They capture individual properties at a high level but nevertheless sacrifice some fidelity to reality for the sake of analytical tractability. While agent-based models are less tractable, they are able to make concrete predictions about how systems behave in the lab--their results are easier to interpret for the non-theorist. This mini symposium will feature talks discussing lattice and agent-based models about specific biological systems, showing the relevance of such models today. How results therein can be interpreted and mapped to reality will also be discussed.

Bhargav Karamched

(Florida State University, United States of America)
"Spatial Model of Oncolytic Virotherapy: Targeting Drug-Resistant Mutants"
Oncolytic virotherapy has emerged as a viable treatment for cancers. Although successful cancer treatments with viruses have been observed, they are few and far between. Here, we explore whether combining virotherapy with other methods of cancer treatment may lead to more robust, reliable cancer treatment. For example, cancer cells sometimes undergo mutations that allow them to develop resistance to treatment drugs. To address such a mutation, we explore the possibility of targeting drug-resistant mutants with viruses so that standard drug treatments of cancerous tumors may be used to target cancerous cells. We develop a lattice model that describes cancer tumor growth dynamics and mutant cell dynamics. We find that when mutant cells have a disadvantageous mutation, virus infection amplifies the nature of the disadvantage, with a slight caveat. When infectivity is too high, the population-level death rate is increased so that for a tumor to reach a given size, more cell divisions are necessary. This leads to the presence of more mutants than when no virus is present. We explore this nuanced system with a mean field equation and discuss how viruses used in such a way can progress cancer treatments in the future.

Cicely Macnamara

(University of St Andrews, Scotland)
" Computational modelling and simulation of tumour growth and development within a 3D heterogeneous tissue"
The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Cancer cells can arise from any type of cell in the body; cancers can grow in or around any tissue or organ making the disease highly complex. My research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modelling. In this talk I shall present a 3D individual-based force-based model for tumour growth and development in which we simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent is fully realised, for example, cells are described as viscoelastic sphere with radius and centre given within the off-lattice model. Interactions are primarily governed by mechanical forces between elements. However, as well as he mechanical interactions we also consider chemical interactions, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells, as well as intercellular aspects such as cell phenotypes.

Hamid Teimouri

(Rice University, United States of America)
"The impact of the temporal order of mutations on cancer initiation dynamics"
Cancer is a set of genetic diseases that are driven by mutations. It was recently discovered that the temporal order of genetic mutations affects the cancer evolution and even the nature of the disease itself. The mechanistic origin of these observations, however, remain not well understood. We present a theoretical model for cancer initiation dynamics that allows us to quantify the impact of the temporal order of mutations. In our approach, the cancer initiation process is viewed as a set of stochastic transitions between discrete states defined by the different numbers of mutated cells. Using a first-passage analysis, probabilities and times before the cancer initiation are explicitly evaluated for two alternative sequences of two mutations. It is found that the probability of cancer initiation is determined only by the first mutation, while the dynamics depends on both mutations. In addition, it is shown that the acquisition of a mutation with higher fitness before mutation with lower fitness increases the probability of the tumor formation but delays the cancer initiation.

Namiko Mitarai

(University of Copenhagen, Denmark)
"Emergence of diversity in a model ecosystem of sessile species with mutually exclusive interactions"
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a lattice model ecosystem of sessile (immobile) and mutually excluding organisms competing for space. The competition is controlled by an interaction network with fixed links chosen randomly. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that patches of isolated meta-population spontaneously formed by the collapse of cyclic relations are essential for the transition to the state of high diversity. The high-diversity state is robust against small disturbance or spontaneous death. When new species evolve by mutating the species interaction network from ancestry species, the high-diversity state appears as long as there is a cost associated with the ability to invade another species.

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Virtual conference of the Society for Mathematical Biology, 2021.